David Tong: Classical Dynamics

David Tong: Lectures on Classical Dynamics

This is a second course in classical mechanics, given to final year undergraduates. They were last updated in January 2015. Individual chapters and problem sheets are available below. The full set of lecture notes, weighing in at around 130 pages, can be downloaded here:

PostScript      PDF      HTML

A more basic course on classical dynamics, covering Newtonian mechanics and special relativity, can be found here.


  • 1. Newtonian Mechanics:   PDF
    Table of Contents; Introduction; Newtonian mechanics for a single particle and many particles
  • 2. The Lagrangian Formulation:   PDF
    The principle of least action; Changing coordinate systems; Constraints and generalised coordinates; Noether's theorem and symmetries; Applications; Small oscillations and stability
  • 3. The Motion of Rigid Bodies:   PDF
    Kinematics; The inertia tensor; Euler's equation; Free tops; Euler's angles; The heavy symmetric top; The motion of deformable bodies
  • 4. The Hamiltonian Formulation:   PDF
    Hamilton's equations; Liouville's theorem; Poincare recurrence theorem; Poisson brackets; Canonical transformations; Action-angle variables; Adiabatic invariants; Hamilton-Jacobi theory; Relationship to quantum mechanics

Problem Sheets

  • Problem Sheet 1:   Postscript    PDF    Lagrangian Formulation

  • Problem Sheet 2:   Postscript    PDF    Normal Modes, Inertia Tensors and Rotations

  • Problem Sheet 3:   Postscript    PDF    Euler's Equations and Euler Angles

  • Problem Sheet 4:   Postscript    PDF    Hamiltonian Formulation